Basis of polynomial

I knew that a polynomial of degree n has n+1 basis, i.e 1,x,x^2...x^n;
But what if a0=0,i.e the constant term is 0, like x^3+x, then what is the dimension and the basis? Is there only x(one dimension) as the basis?

I knew that a polynomial of degree n has n+1 basis, i.e 1,x,x^2...x^n;
But what if a0=0,i.e the constant term is 0, like x^3+x, then what is the dimension and the basis? Is there only x(one dimension) as the basis?